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J. 4) Proposition. Let X and (E,E). Suppose that PK(X,,) Then 5 = S. H X and X be right processes with the same state space = FK(X,,) for each x E E and compact K C E. are transient, then the equality 5 = S implies that PB(x,·)=FB(X,,) for all xEE and BEE. Proof. 33]. The converse for transient processes is proved on page 553 of [Fl]. (8t w) identically in t,s,and w. 19}, for example) this entails no loss of generality. We are now prepared to state BGM for transient processes. 5) Theorem. ) for each x E E and BEE.